This project is designed to use mathematical and computational methods to develop models based on experimental data of the morphology and function of individual dendrites, whole neurons, and neuron networks. We have now completed development of a remarkably simple model approach that can successfully reproduce the complex three-dimensional morphology of adult cat spinal motoneurons using just two parameters. The result suggests that the direction in which a dendritic branch projects away from a branching point depends in part on the direction of its parent branch and in part on the radial direction of the branch point away from the cell soma. This radial ?tropism? is presumably related to mechanical constraints imposed by the external environment surrounding motoneuron dendrites. This project required development and validation of novel approaches to measure the three-dimensional architecture of neuron dendrites in order to constrain the model parameters and to compare simulated with actual neurons.[unreadable] Natural neuronal dendrites exhibit irregular, meandering trajectories that have received little previous attention. We have developed a modified fractal analysis technique that allows us to measure meandering trajectories quantitatively and to reproduce them with high fidelity. The simulation algorithm requires only two parameters. Our 3D simulations of complete motoneurons, including 3D tree structure and meandering branch trajectories, closely approximate the actual motoneurons on which they are based despite the fact that only four parameters, all based on actual data, are used. As we have shown previously, such parsimonious descriptions can be valuable in revealing biological constraints under which neurons form and are maintained. Two research reports on this work have been submitted to the Journal of Comparative Neurology.